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24 Three circles lie on the straight line and touching each other as shown in the diagram ， at which a,b and c are the radii of circle A, B and C respectively.. Find the value of c in te[r]
(1)Full Name： Year:
IC No: Date： Time：
School Name：
Rules and Regulations (Please read these rules and regulation carefully)
1 Please fill in your FULL name correctly, IC No, school name and the date and time of contest clearly in the spaces above Those who not fill in the required particulars will be disqualified automatically
2 Do not open the question booklet until you are told to so You may only use 2B pencil when answering the questions
3 No calculators and any unauthorised electronic devices (including mobile phones) are allowed during the contest
4 Strict silence must be observed at all times in the examination hall and please be reminded that youMAY NOTleave your seat without permission
5 If you have any request or enquiry, please raise your hand and wait for an invigilator
6 Only one candidate is allowed to leave the hall at a time You are required to return to the hall within 10 minutes or else you will automatically be disqualified from the contest
7 Each question in the contest have been verified by experienced trainers, thus no further explanation will be given
8 The time allowed for the paper is120 minutes You must stop writing when you are told to so You MUST fill in your answer in the answer sheet provided in second page of the question
booklet You will not be awarded marks for any answer written in the question booklet
10 Please be reminded that this is a contest and not an examination, not expect to answer all types of questions
11 Please tear off the answer sheet carefully and returned to invigilator along with contest paper Participant only can bring back the contest papers on next week.
Scoring System
1.ForQuestion 1- 10, markswill be awarded for each correct answer ForQuestion 11- 20, markswill be awarded for each correct answer ForQuestion 21- 25, markswill be awarded for each correct answer However, you will NOT be penalised for each incorrect answer
(2)5 If 20201515 2p3q5r, then pqr ?
(3 markah) 1 Calculate:
(20152015)(20142014) )
20142015 )(
20152014 (
(3 markah)
2 Calculate:
2014)2 (2014 2015)2 (2014 2015)3
2015 (
(3 markah)
3 If (2+√ x)=3, what is the value of x?
(3 markah)
4 The value of M is and M is 30% of Q, Q is 20% of P, and N is 50% of P. What is the value of N?
(3)7 Simplify
( + + ) ( + - ) ( - + ) ( + + )
(3 markah) 6 Six numbers from a list of nine integers are 7, 8, 3, 5, and What is
the largest possible value of the median of the nine numbers in the list?
(3 markah)
9 In the diagram below ABC is a right-angled triangle
cm AC
cm AB
B90, 6 , 10
Line AB is used as a diameter to
draw a semicircle, while line BC is used as a diameter to draw
another semicircle Calculate the area of the shaded region in term of
(3 markah) 8 Some identical cubes are glued tightly together as shown in the diagram
The volume of the solid formed in this way is 189 cm3 The surface area of the solid, in cm2, is
(4)10 = = = k, then what is the value of k ?
(3 markah)
13 AB is a chord in a circle with center O and radius 39 cm. The point N divides the chord AB such that AN =56 cm and NB = 16 cm Find the length ON in cm
(4 markah)
14 If M = (│x – │+│x│– ), find the range of M
(4 markah) 12 If 65 1 1 , 2015 a c c b b a b a c b a
Solve ?
b c
a a c b b a c (4 markah) 11 There are 300 white boxes and n red boxes in storage Each box
contains the same number of soccer balls The total number of soccer balls in all of the boxes is n + 290n − 2490 Determine n
(4 markah)
A
(5)16 As shown in the diagram, line AB is parallel to line CD and line EI is perpendicular to line EG EF≠FG≠EH≠HI How many complementary angles of angle EHF
(4 markah)
17 In the diagram below A,B,C,D,E,F and G are plotted along the circle with centre O, and line AB is the diameter of the circle Given that
, 15 ,
20
find
(4 markah) 15 Given that f(x) = ax³ + bx² + cx + d, If x takes the value of its opposite
number, the corresponding value of f(x) is also the opposite number,and f(-1) = 0, then find the value of
(4 markah)
18 Real number a,b,c fulfill the equation below,
0 2 2 2
2 b c ab bc c a
Find the value ofa+b+c
(4 markah) B
A
C D
E
F H
(6)1 22 An order pair of rational number x and y is defined as (x,y) If xy < and satisfied the equations below
3 │x│y + x = and │x│+│y│=
then, determine the values of order pairs of x and y
(6 markah) 23 Find the remainder of when it is divided by 11
(6 markah) 21 Solve the following equation :
(6 markah)
+ + +… = 2014
20 A circle passes through vertices A and B and touches side DC of a square If the square has side length units, then the radius of the circle is
(4 markah)
19 Given that ,
2 5
x Find value of 5
3 1
x x x
(4 markah)
A
B
C D
B
(7)24 Three circles lie on the straight line and touching each other as shown in the diagram，at which a,b and c are the radii of circle A, B and C respectively Find the value of c in terms of a and b
(6 markah)
25 Given that the point P is outside the equilateral triangle ABC.But inside the region of∠ABC If the distance from P to BC,CA,AB are
, and respectively, and - + = cm, Find the the area of△ABC
(6 markah)
●
●
●
A
B
C
a b
c